When stormtroopers get into fire fights with the rebels, I noticed that a few are killed after a single shot to the chest. Is their armor not really armor or are the rebels guns just that powerful? In some of the books in Legends, it seems they can take more of a beating but in the original movies they can't seem to take as much. Do some stormtroopers have different grades of armor?

Based solely on what we see in the original trilogy, Stormtrooper armor was terrible- virtually useless, in fact. Not only do blasters cut through it like a hot knife through butter, but Ewoks kill troopers using nothing more than arrows, clubs, and rocks. At one point, Han punches a trooper in the face and knocks him out cold. As a general rule, if your armor doesn't protect you from rocks, sticks, and fists, it isn't worth wearing.
– Wad CheberJun 8 '15 at 2:45

That "really great article" is fun, but it's worthless. It refers to S.L.A.M Marshall's "Men Against Fire" and misses the point. It even goes on to state "With that conditioning" men have trouble shooting other people. What conditioning? After the publication of "Men Against Fire", military training was modified to overcome the problem. By the Korean war, US troops under fire shot back half the time. By Vietnam, the rate was essentially 100%, and has remained at that level. It's just not that hard to get people to kill, once you understand the problem.
– WhatRoughBeastJun 7 '15 at 19:37

The "with that conditioning" you're referring to is the propaganda push to dehumanize enemies. Perhaps the Empire never took steps to correct this problem. Perhaps it never thought it would need to, since body armor may be so prevalent in the Star Wars universe that you'd rarely find your troops in a firefight against unarmored faces to look at. Regardless, you make a good point that this effect can be overcome and maybe isn't the best explanation
– childcat15Jun 7 '15 at 22:00

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And yet Ewoks kill troopers in full body armor using sticks and rocks.
– Wad CheberJun 8 '15 at 2:46

@WadCheber Against armor, blunt force weapons can be more effective than piercing weapons. Qoute: "the force of a blow from a mace is great enough to cause damage without penetrating the armour", from: en.wikipedia.org/wiki/Mace_(club) Also, we saw storm troopers distracted and/or incapacitated by Ewoks, but never clearly killed.
– Todd WilcoxSep 11 '15 at 14:53

The Stormtroopers' armor, out-of-universe, was inspired by and roughly equivalent to flak jackets. Flak jackets protected mainly against exactly what they were named for - flak (shrapnel) - but because Kevlar hadn't become commercially viable as a bullet-resistant material until the late 70s (about when Star Wars was filmed, not written) the jackets were bulky, affecting mobility. They also weren't bulletproof; most rifle rounds could penetrate them (and in fact the same is true for modern Kevlar police vests; a .308 or .30-06 FMJ hunting round can infrequently penetrate them even though civilian bullets are specifically designed not to be armor-piercing)

Back over in G-canon, you now have to protect a trooper from a blaster bolt; a packet of plasma in a self-contained magnetic field that explodes on contact with most solid objects. There are various materials that provide adequate blast shields, such as Mandalorian iron, but equipping billions of stormtroopers across the galaxy with suits made of these highly-prized,rare, expensive materials simply isn't feasible. So, the Empire went with the "flak jacket" concept of a suit designed to deflect glancing and minor hits, but a direct hit from a more powerful weapon would be able to penetrate it. That's fine; as with GAR clone troopers before them there are plenty more stormtroopers where that one came from. As stated by the other Keith, the suits also had environment-survival features, including the ability to survive in open space for a time. That usually requires full enclosure, not just the front-and-back armored vest.

Lastly, regarding stormtrooper aim: Not sure if you've ever been in a firefight (if you haven't, thank your lucky stars and the next soldier you meet), but the hit percentage statistics among police officers in shootouts is really low, something like 15% of all shots fired hitting their intended target. There are some notable incidents where criminals AND officers empty their guns at point-blank range and don't hit each other. Soldiers in combat may fire hundreds of rounds at an enemy position just to make the other guys keep their heads down. While there are some necessary rules regarding the survival rate of your main characters in combat (they don't get to be heroes if they die in the initial skirmish 2 hours before the final climactic scene), various accounts of real shootings generally lend credence to the argument that when your adrenaline's going and you could die any second, your aim suffers.

In all versions of the Star Wars Roleplaying Game the armor of Stormtroopers is excellent. A kind of sci-fi half-plate (very heavy armor) still allowing mobility.

I think the movie just needed show-effects, so one can consider the shot chest just like a head-shot. In an age of limited special-effects it was a cheap way to show who received a fatal hit.

Rebel Blasters (handgun version, like Han Solo used) are possibly stopped by heavy armor. The rifle version is already much more penetrating and damage-dealing.

The Lightsaber then really cuts-through nearly any armor. Lightsabers do enormous damage, even without special force-abilities. There is a reason, beyond optics, why Jedi & Sith needed no other weapons, when they learned wielding light-sabers. ;)